Fluid Mechanics

JEE Main level, single correct, medium

41 of 192

Question 41 of 192

A cubical block of side 0.5m0.5m floats on water with 3030% of its volume under water. What is the maximum weight that can be put on the block without fully submerging it under water?

[Take, density of water =103kg/m3={10}^{3}kg/{m}^{3} ]

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Answer: (A) 87.5kg87.5kg

In first case, when 3030% of the cube inside water,
ρwVing=ρcVg{\rho }_{w}{V}_{in}g={\rho }_{c}Vg
VinV=ρcρw=0.3\dfrac{{V}_{in}}{V}=\dfrac{{\rho }_{c}}{{\rho }_{w}}=0.3
Additional weight we can put ww is,
Vρwg=ρcVg+wV{\rho }_{w}g={\rho }_{c}Vg+w
w=V(ρw−ρc)gw=V\left({\rho }_{w}-{\rho }_{c}\right)g
=(0.5)3×0.7×103×g={\left(0.5\right)}^{3}\times 0.7\times {10}^{3}\times g
=87.5gN=87.5g N
Addition of mass that we can put =87.5kg=87.5 kg

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